Question: Let F(x) = a u(x) (t) dt for the specified a, u, and . Use a CAS to perform the following steps and answer

Let F(x) = ∫au(x) ƒ(t) dt for the specified a, u, and ƒ. Use a CAS to perform the following steps and answer the questions posed.

a. Find the domain of F.

b. Calculate F′(x) and determine its zeros. For what points in its domain is F increasing? Decreasing?

c. Calculate F″(x) and determine its zero. Identify the local extrema and the points of inflection of F.

d. Using the information from parts (a)–(c), draw a rough handsketch of y = F(x) over its domain. Then graph F(x) on your CAS to support your sketch.

a = 0, u(x) = 1 - x2, ƒ(x) = x2 - 2x - 3

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